Abstract
The absence of ergodicity is investigated analytically and numerically for classical field theories and for Euler equations in two dimensions. In this case the authors extend the arguments of Patrascioiu (1984) to inviscid two-dimensional fluid dynamics. They comment on the risks of truncation introduced by a numerical simulation of continuous systems reflecting on the analytical properties of the solution of the field equations. It appears that ergodicity is a property only of the discretised problem. The considerations are tested on a simple model of a radiant cavity, which shows the absence of the ultraviolet catastrophe and the possibility of wrong interpretations of numerical simulations of field theories.
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